Question: Simplify the following expression: $ n = \dfrac{-7z - 5}{2z - 2} - \dfrac{-1}{2} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-7z - 5}{2z - 2} \times \dfrac{2}{2} = \dfrac{-14z - 10}{4z - 4} $ Multiply the second expression by $\dfrac{2z - 2}{2z - 2}$ $ \dfrac{-1}{2} \times \dfrac{2z - 2}{2z - 2} = \dfrac{-2z + 2}{4z - 4} $ Therefore $ n = \dfrac{-14z - 10}{4z - 4} - \dfrac{-2z + 2}{4z - 4} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-14z - 10 - (-2z + 2) }{4z - 4} $ Distribute the negative sign: $n = \dfrac{-14z - 10 + 2z - 2}{4z - 4}$ $n = \dfrac{-12z - 12}{4z - 4}$ Simplify the expression by dividing the numerator and denominator by 4: $n = \dfrac{-3z - 3}{z - 1}$